Invariants of unipotent transformations acting on noetherian relatively free algebras

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dc.creatorDrensky, Vesselin
dc.date2004-05-21
dc.date.accessioned2026-07-07T06:29:39Z
dc.date.available2026-07-07T06:29:39Z
dc.descriptionThe classical theorem of Weitzenboeck states that the algebra of invariants of a single unipotent transformation $g$ in $GL_m(K)$ acting on the polynomial algebra $K[x_1,...,x_m]$ over a field $K$ of characteristic 0 is finitely generated. Recently the author and C.K. Gupta have started the study of the algebra of $g$-invariants of relatively free algebras of rank $m$ in varieties of associative algebras. They have shown that the algebra of invariants is not finitely generated if the variety contains the algebra $UT_2(K)$ of $2\times 2$ upper triangular matrices. The main result of the present paper is that the algebra of invariants is finitely generated if and only if the variety does not contain the algebra $UT_2(K)$. As a by-product of the proof we have established also the finite generation of the algebra of $g$-invariants of the mixed trace algebra generated by $m$ generic $n\times n$ matrices and the traces of their products.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0405404
dc.identifierhttp://arxiv.org/abs/math/0405404
dc.identifierSerdica Math. J. 30 (2004), Nos. 2-3, 395-404
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98111
dc.subjectRings and Algebras
dc.subjectCommutative Algebra
dc.subject16R10 (primary); 16R30 (secondary)
dc.titleInvariants of unipotent transformations acting on noetherian relatively free algebras
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